Adaptive Methods for Form Error Determination in Discrete Point Metrology.

The two most important factors in sampling during coordinate verification of a surface are the number of measuring points that represent the surface accurately, and the distribution of those points. In this work, sampling of free form surfaces and flat plates is studied and some techniques are developed for this purpose. Three algorithms are developed in this work for sampling of free form surfaces at a patch scale (not the entire surface). The three developed algorithms take each patch on the surface as a separate unit and distribute the points within the patch in two steps: sample the most critical points that depend on maximum and minimum Gaussian curvature of each patch and add more points depending on the overall distribution of the most critical points distributed on the surface. In each step of sampling, the maximum difference between the CAD model and the surface created using those sampled points is obtained, and an efficient (reduced) number of measuring points is determined. This minimizes sampling effort and (non-value-added) measurement time. A comparison is performed between the three proposed algorithms against two well known sampling techniques; the equiparametric approach, and the patch-size-based sampling method. The proposed algorithms distribute the points in each patch based on a specific plan. The results show that the developed algorithms help select an efficient number of sampling points. Adaptive sampling for determining flatness and form errors found in end milled parts is studied. The well-known model of Kline et al. (1982) is modified to generalize the modeling of the workpiece errors in milling flat plates. The change in the inertia, of the cutter and the workpiece, before and after the cutting process is added to the cutting force model developed by Kline et al. (1982). The additional term made the cutting force and the cutter deflection model more accurate and closer to the actual measurements of forces and cutter deflection. The force obtained from the modified model is applied theoretically, using a finite element analysis by ANSYS, on a flat plate to obtain the workpiece deflection at specific points. The cutter deflection and the workpiece deflection are added to obtain the dimensional error on the flat plate. Thus, the sampling points are obtained on the flat plate. Those sampling points are used in this adaptive sampling procedure proposed. The adaptive sampling procedure supposes that if the tolerance zone for a specific area is high, then there is a good likelihood of finding points of high dimensional errors in the neighborhood of that area. An efficient number of sampling points is determined using this supposition. The tolerance zone obtained is compared to that obtained using a uniform grid of points. A tolerance zone, with significant reduction in number of points (26 points) compared to (312 points) with 89.5% accuracy, has been obtained. Results show that even at a reduced number of points, good accuracies are achieved in form error determination.